Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set: 52

Answer

$40+13i$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (5-6i)(2+5i) ,$ simplifies to \begin{array}{l}\require{cancel} 5(2)+5(5i)-6i(2)-6i(5i) \\\\= 10+25i-12i-30i^2 \\\\= 10+13i-30i^2 \\\\= 10+13i-30(-1) \\\\= 10+13i+30 \\\\= 40+13i .\end{array}
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